onsider the triangle to the right.

a. Write an equation that can be used to find the value of y.
b. What is mangle∠​K?
Upper LL
Upper MM
Upper KK
56 degrees56°
left parenthesis 5 y minus 19 right parenthesis degrees(5y−19)°

Question content area bottom
Part 1
a. Write the equation below.
5 y minus 19 equals 565y−19=56
​(Do not simplify. Do not combine like​ terms.)
Part 2
b. What is mangle∠​K?

1 answer

To solve the problem, we first analyze the information presented:

  1. It mentions the angle measure \( \angle K \) along with \( (5y - 19)^\circ \) and \( 56^\circ \).
  2. Typically, in a triangle, the sum of the angles must equal \( 180^\circ \).

Part 1:

We are tasked with writing an equation to find the value of \( y \). Considering the angle measures given and understanding that they are part of a triangle, we can use the equations provided.

To find \( y \), we can set up the equation as provided:

\[ 5y - 19 = 56 \]

Part 2:

To find \( \angle K \), we only need the expression for \( \angle K \) if we substitute the value of \( y \).

Starting with the equation we wrote:

  1. From the equation: \[ 5y - 19 = 56 \]

  2. Solve for \( y \): \[ 5y = 56 + 19 \] \[ 5y = 75 \] \[ y = 15 \]

  3. Finding \( \angle K \): Now we substitute \( y \) back into \( \angle K \): \[ \angle K = 5y - 19 \] Substituting \( y = 15 \): \[ \angle K = 5(15) - 19 = 75 - 19 = 56^\circ \]

Thus:

  • The answer to Part 1 is: \[ 5y - 19 = 56 \]

  • The answer to Part 2 is: \(\angle K = 56^\circ\)